With recent digitalization of multimedia information, the importance of arithmetic processing algorithms and arithmetic processing circuits that implement digital signal processing has been increasing. Especially, digital filters are used to eliminate noise, adjust frequency characteristics, separate signals, and so on. FIR filters having finite impulse response ensure stability always against bounded input. If the impulse response is symmetrical, the FIR filters can implement perfect linear phases. The linear phases are important characteristics in waveform transmission, measurement, sound reproduction, and so on. However, because of the trade-off between precision required in the frequency characteristics of the filter and the scale of the filter, high-order transfer characteristics are required to obtain steeper attenuation characteristics, and the circuit requires a large number of multipliers and delay elements. To create a pass-band filter with a very narrow band, for example, a very high degree of transfer characteristics is required, and a large number of multipliers are required accordingly.
In that context, many propositions have been made. Non-patent literature 1 describes the Remez method as a conventional method that has been used usually. Non-patent literature 2 describes a method of configuring a low-sensitivity linear-phase FIR filter by cascade connection, and the cascade connection allows the number of multipliers to be reduced. Patent literature 1 describes an FIR filter provided to vary the delay of the filter output signal.
Moreover, FIR filters for various uses such as filters for separating acoustic signal bands and filters for eliminating noise in image have been studied.
There are more conventional technologies. For example, non-patent literature 3 discloses the design and implementation of oversampled filter banks for multilevel FIR filters with low aliasing.
Non-patent literature 4 discloses a filter bank with desired frequency response and low aliasing noise. Non-patent literature 5 discloses a realization of oversampled cosine modulated filter banks with perfect reconstruction.
Patent literature 2 discloses a filter bank and filtering method that can efficiently implement critically sampled filter banks for real-value signals and especially a cosine modulated filter bank.